A manifesto for the computational method
Theoretical Computer Science
Preemptive Scheduling with Rejection
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
A FPTAS for Approximating the Unrelated Parallel Machines Scheduling Problem with Costs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Bin packing problems with rejection penalties and their dual problems
Information and Computation
Online scheduling in a parallel batch processing system to minimize makespan using restarts
Theoretical Computer Science
Computers and Industrial Engineering
Online scheduling with machine cost and rejection
Discrete Applied Mathematics
A fast asymptotic approximation scheme for bin packing with rejection
Theoretical Computer Science
Theoretical Computer Science
An Optimal Incremental Algorithm for Minimizing Lateness with Rejection
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Online unit clustering: Variations on a theme
Theoretical Computer Science
Bounded single-machine parallel-batch scheduling with release dates and rejection
Computers and Operations Research
A PTAS for parallel batch scheduling with rejection and dynamic job arrivals
Theoretical Computer Science
Scheduling with Rejection to Minimize the Makespan
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Discrete Applied Mathematics
Bin packing problems with rejection penalties and their dual problems
Information and Computation
Minimizing the makespan on a single parallel batching machine
Theoretical Computer Science
Single-machine scheduling under the job rejection constraint
Theoretical Computer Science
Bounded parallel-batch scheduling on unrelated parallel machines
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Lorenz versus Pareto dominance in a single machine scheduling problem with rejection
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Online scheduling with rejection and withdrawal
Theoretical Computer Science
Optimal semi-online algorithm for scheduling with rejection on two uniform machines
Journal of Combinatorial Optimization
On several scheduling problems with rejection or discretely compressible processing times
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Inventory and facility location models with market selection
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Bin packing with rejection revisited
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
Scheduling on parallel identical machines with job-rejection and position-dependent processing times
Information Processing Letters
A fast asymptotic approximation scheme for bin packing with rejection
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
International Journal of Applied Evolutionary Computation
Noncooperative Games for Subcontracting Operations
Manufacturing & Service Operations Management
A survey on offline scheduling with rejection
Journal of Scheduling
Semi-online scheduling on two identical machines with rejection
Journal of Combinatorial Optimization
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We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by $m$ identical parallel machines and a set of $n$ jobs, with each job characterized by a processing time and a penalty. In the on-line version the jobs become available one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs.The main result is a $1+\phi\approx 2.618$ competitive algorithm for the on-line version of the problem, where $\phi$ is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all $m$. For fixed $m$ we give improved bounds; in particular, for $m=2$ we give a $\phi\approx 1.618$ competitive algorithm, which is best possible.For the off-line problem we present a fully polynomial approximation scheme for fixed $m$ and a polynomial approximation scheme for arbitrary $m$. Moreover, we present an approximation algorithm which runs in time $O(n\log n)$ for arbitrary $m$ and guarantees a $2-\frac{1}{m}$ approximation ratio.